Maxwell’s Equations (so far) Gauss’s law Gauss’ law for magnetism Faraday’s law Ampere’s law*

Parallel-Plate Capacitor Revisited B=0 ? Not experimentally! For surface S1, Is = I, but for surface S2, Is = 0 Q -Q Wait, LHS is the same (because C is the same)! ?? You could make this work if a fictitious current Id is added to Is in such a way that Id is zero for S1 but is equal to I for S2. will work.

James Clerk Maxwell proposed that a changing electric field Displacement Current James Clerk Maxwell proposed that a changing electric field induces a magnetic field, in analogy to Faraday’s law: A changing magnetic field induces an electric field. Ampere’s law is revised to become Ampere-Maxwell law is the displacement current. where The direction of the displacement current is the same as that of the electric flux, if the flux increases, and is opposite, if the flux decreases.

Basis for electromagnetic waves! Maxwell’s Equations Basis for electromagnetic waves! The equations are often written in slightly different (and more convenient) forms when dielectric and/or magnetic materials are present.

©2008 by W.H. Freeman and Company

DOCCAM 2

Electromagnetic Waves From Faraday’s Law

©2008 by W.H. Freeman and Company

Electromagnetic Waves From Ampère’s Law

©2008 by W.H. Freeman and Company

Electric Dipole Radiation

©2008 by W.H. Freeman and Company

WARM UP QUIZ 1 Light is an electromagnetic wave where the wavelength λ in meters times the frequency f in Hz is equal to the velocity of light c = 3 x 108 meters/second in vacuum. Which of the following statements is correct? λ = 100 meters, f = 1x106 Hz (b) λ = 105 meters, f = 3x104 Hz λ = 10-6 meters, f = 3x1014 Hz λ = 1 meter, f = 3/2 x 108 Hz

Electromagnetic Wave Propagation in Free Space So, again we have a traveling electromagnetic wave speed of light in vacuum Ampere’s Law Faraday’s Law Wave Equation Speed of light in vacuum is currently defined rather than measured (thus defining meter and also the vacuum permittivity).

Plane Electromagnetic Waves where c Transverse wave Plane wave (points of given phase form a plane) Linearly polarized (fixed plane contains E) x

Energy Density of Electromagnetic Waves Electromagnetic waves contain energy. We know already expressions for the energy density stored in E and B fields: EM wave So Total energy density is

Energy Propagation in Electromagnetic Waves Energy flux density = Energy transmitted through unit time per unit area Intensity I = Average energy flux density (W/m2) Define Poynting vector Direction is that of wave propagation average magnitude is the intensity

If radiation is totally absorbed: Radiation Pressure Electromagnetic waves carry momentum as well as energy. In terms of total energy of a wave U, the momentum is U/c. During a time interval Δt , the energy flux through area A is ΔU =IA Δ t . If radiation is totally absorbed: If radiation is totally reflected: x2 momentum imparted radiation pressure EXERTED

Light is an Electromagnetic Wave Maxwell’s Rainbow Light is an Electromagnetic Wave

x The direction of travel Physics 241 10:30 Quiz 2 An electromagnetic wave is traveling in +x direction and the electric field at a particular point on the x-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the magnetic field? a) -z b) -x c) -y d) +y e) None of the above z E y x The direction of travel is that of E x B.

z a) +x E y b) -x c) -y B x d) -z e) None of the above Physics 241 11:30 Quiz 2 An electromagnetic wave is traveling through a particular point in space where the direction of the electric field is along the +z direction and that of the magnetic field is along the +y direction at a certain instant in time. Which direction is this wave traveling? z E y B x The direction of travel is that of E x B. a) +x b) -x c) -y d) -z e) None of the above

z -z B -x y c) -y x d) +x e) None of the above Physics 241 – Quiz 21c – April 2, 2009 An electromagnetic wave is traveling in +y direction and the magnetic field at a particular point on the y-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the electric field? z B y x The direction of travel is that of E x B. -z -x c) -y d) +x e) None of the above

READING QUIZ 1 The extended Amperes law involves a displacement current which was added to the real currents as a source of the magnetic (B) fields. Which of the following statements is correct? A| the displacement current has a constant magnitude ie not a frequency dependent magnitude. B| The displacement current does not involve the constant εO= 1/4πk. C| The displacement current is proportional to εO. D| The displacement current was introduced by Faraday.